Applying Gaussian distributed constraints to Gaussian distributed variables
This addresses the need for efficient handling of uncertain constraints in applications like Kalman filtering, though it is incremental as it builds on existing truncation methods.
The paper tackles the problem of truncating Gaussian distributed variables under inequality constraints that are also Gaussian, developing an analytical method with moment-based Gaussian approximations. In a simulation, it outperforms unconstrained Kalman filtering by over 40% and hard-constrained filtering by over 17%.
This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard constraints, or use numerical methods to handle uncertain constraints. The proposed approach introduces moment-based Gaussian approximations of the truncated distribution. This method can be applied to numerous problems, with the motivating problem being Kalman filtering with uncertain constraints. In a simulation example, the developed method is shown to outperform unconstrained Kalman filtering by over 40% and hard-constrained Kalman filtering by over 17%.